Maximum and antimaximum principles for the p-Laplacian with weighted Steklov boundary conditions
Date
2020-03-02
Authors
Cuesta, Mabel
Leadi, Liamidi
Nshimirimana, Pascaline
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
We study the maximum and antimaximum principles for the p-Laplacian operator under Steklov boundary conditions with an indefinite weight
-Δpu + |u|p-2 u = 0 in Ω,
|∇u|p-2 ∂u/∂v = λm(x)|u|p-2 u + h(x) on ∂Ω,
where Ω is a smooth bounded domain of ℝN, N > 1. After reviewing some elementary properties of the principal eigenvalues of the p-Laplacian under Steklov boundary conditions with an indefinite weight, we investigate the maximum and antimaximum principles for this problem. Also we give a characterization for the interval of the validity of the uniform antimaximum principle.
Description
Keywords
p-Laplacian, Steklov boundary conditions, Indefinite weight, Maximum and antimaximum principles
Citation
Cuesta, M., Leadi, L., & Nshimirimana, P. (2020). Maximum and antimaximum principles for the p-Laplacian with weighted Steklov boundary conditions. <i>Electronic Journal of Differential Equations, 2020</i>(21), pp. 1-17.
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Attribution 4.0 International
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This work is licensed under a Creative Commons Attribution 4.0 International License.